With the exception of light, waves are undulations in some material medium. For instance, waves on a slinky are either transverse, in that the motion of the material of the slinky is perpendicular to the orientation of the slinky, if you vibrate the slinky like a rope, or they are longitudinal, with material motion in the direction of the stretched slinky, if you treat it like a spring. (See image on right) Ocean waves are simultaneously transverse and longitudinal, the net effect being (nearly) circular undulations in the position of water parcels. The oscillations in neighboring parcels are phased such that a pattern moves across the ocean surface. Some media support only longitudinal waves, others support only transverse waves, while yet others support both types. Sound waves are purely longitudinal in gases and liquids, but can be either type in solids.

Mechanical transverse waves require a material medium and propogate by means of vibrations of the medium perpendicular to the direction of travel. Examples are water waves, ripples, seismic shear waves, and waves in stretched strings as above.

Electromagnetic (EM) waves (such as light) are also transverse waves but they do not require a medium and thus can pass through a vacuum (see intro).They consist of oscillating electric (E) and magnetic (B) fields which are perpendicular to the direction of propogation while also being mutually perpendicular. EM waves are a disturbance of space itself, which can be thought of as being stretched and therefore being elastic and having a tension. The B and E fields are in phase as shown on the left.

The fundamental S.I. unit of length (meter) is defined in terms of the speed of light in vacuum and the definition of the unit of time, the second. The previous definition was in terms of the wavelength of a particular color of light in the line spectrum of Krypton 86. The modern definition is more accurate as well as being the same to all observers regardless of their relative velocity.

Longitudinal waves propogate by means of vibrations or disturbances in the medium that are in the same direction that the wave travels. Examples are sound (as above), seismic shock waves, slinky springs and part of the motion in ocean waves. Sound waves are a series of high-pressure compressions and low-pressure rarefaction (for this reason, sound is sometimes called a pressure wave). While it might be convenient to think of individual molecules vibrating back and forth around an equilibrium position (producing areas of high and low pressure), the individual molecules in a gas generally move randomly, and it is only in large numbers that this pattern is visible. In longitudinal waves, the convention is to describe displacement in the direction the wave is going (the direction of propagation) as positive, and displacement against that direction as negative.

The pressure and displacement of a molecule at a point are 90o{\displaystyle 90^{o}} out of phase, so that, for example, when a molecule is farthest displaced it is in a normal pressure area, while molecules in compressions or rarefactions have displacement close to zero.

Torsional waves consist of a twisting disturbance moving through a medium such as a wire or a rod.